Surface x-ray scattering and scanning-tunneling microscopy experiments reveal novel coarsening behavior of Pb nanocrystals grown on Si(111)-(7 x 7). It is found that quantum size effects lead to the breakdown of the classical Gibbs-Thomson analysis. This is manifested by the lack of scaling of the island densities. In addition, island decay times tau are orders of magnitude faster than expected from the classical analysis and have an unusual dependence on the growth flux F (i.e., tau is approximately 1/F). As a result, a highly monodispersed 7-layer island height distribution is found after coarsening if the islands are grown at high rather than low flux rates. These results have important implications, especially at low temperatures, for the controlled growth and self-organization of nanostructures.